Actually, at the paint shop in Talbotville which is who makes the Crown Vic, this is how it's done. They paint everything separatly - the hood, trunk and doors. My father-in-law is one of their head engineers there and I've seen this personally. I can't speak about other plants, but that is how Ford does it at that particular plant.
Edit: Should have added... That's how it's done if needed. If the whole car is going to be the same colour, then you're right - it's painted together. But when they get orders for different coloured doors or whatever, which happens all the time, it's all done separatly.